Fuzzy goal programming approach on computation of the fuzzy arithmetic mean

Abstract

In the traditional way of computing the arithmetic mean, there are various alternatives that support the same objective. Since the proposal of fuzzy sets by Zadeh, Bellman and Zadeh have developed a basic framework for decision-making in a fuzzy environment and investigated the fuzzy c-mean and the fuzzy weighted averages. The fuzzy c-mean is an extension of the c-mean that is widely applied to cluster algorithm. The fuzzy weighted averages extend the normal weighted mean by using the concept of fuzzy numbers and the extension principle. The fuzzy arithmetic mean is an extension of the normal arithmetic mean. The Goal Programming, which is used to solve the multiple objective decision problems, has wide and great potential among other methods targeting maximization or minimization of goals. The goal programming aims to minimize the biases from each objective, instead of optimizing of goals. In this study we do introduce a new approach to the computation of fuzzy arithmetic mean powered by fuzzy goal programming, named GUMAR.